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<p class="MsoNormal" align="center" style="text-align:center"><b><span style="font-size: 14pt; line-height: 107%; font-family: 'Times New Roman'; ">MASTER’S
THESIS DEFENSE<o:p></o:p></span></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><b><span style="font-size: 12pt; line-height: 107%; font-family: 'Times New Roman'; ">Naveen
Krishnaraj<o:p></o:p></span></b></p>
<p class="MsoNormal" align="center" style="text-align:center"><b><span style="font-family: 'Times New Roman'; ">Implementing a new and
rigorous technique for 1-D NMR Inversion: Slope of L-curve and Adaptive Pruning
<o:p></o:p></span></b></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; "> </span></b></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; ">Date:
</span></b><span style="font-family: 'Times New Roman'; ">Tuesday 1<sup>st</sup>
August 2017<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; ">Location:</span></b><span style="font-family: 'Times New Roman'; "> ERP 9, Room 123<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; ">Time:</span></b><span style="font-family: 'Times New Roman'; "> 1:30 pm – 3:30pm<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><span style="font-family: 'Times New Roman'; "> </span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; ">Committee
Chair: </span></b><span style="font-family: 'Times New Roman'; ">Dr. Michael Myers<b><o:p></o:p></b></span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><b><span style="font-family: 'Times New Roman'; ">Committee
Members: <o:p></o:p></span></b></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><span style="font-family: 'Times New Roman'; ">Dr. Lori Hathon<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="text-align:center;line-height:normal"><span style="font-family: 'Times New Roman'; ">Dr. Alon Arad<o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify;line-height:normal"><span style="font-family: 'Times New Roman'; "> </span></p>
<p class="MsoNormal" style="text-align:justify;line-height:200%"><span style="font-family: 'Times New Roman'; ">1-D NMR data inversion is the process of
obtaining T<sub>2</sub> amplitude distribution from the NMR spin echo trains.
NMR inversion is an ill-posed problem, because of the noise in the data allows for many possible solutions. We solve for the
amplitudes on an equally spaced logarithmic scale, representing typical
pore system distribution. If we simply used a
least square method on this problem the solution is highly unstable, so we adopted a technique called Tikhonov-Regularization
to restrict the range of possible solutions. <o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify;line-height:200%"><span style="font-family: 'Times New Roman'; ">A robust version of this algorithm was developed and detailed parametric studies was performed. Two different L-cure parametrizations, the slope of the L-curve
method and adaptive pruning was implemented. We
generated forward models for the T2 echo train, using an assumption of multiply
peaked amplitude distributions and varying levels of Gaussian white noise. The forward models were then inverted using
the developed algorithm to examine how much of the original information was
lost. We conclude with a discussion of
the limitations of NMR inversion and the relative merits of each L-curve
parametrization. <o:p></o:p></span></p>
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